The present article investigates the rhythm of study as described by Giorgio Agamben in ‘The idea of study’, present in Idea of prose. In this short treatise, Agamben presents Melville’s scrivener Bartleby as the exemplary embodiment of study. Bartleby’s paradigmatic status, according to Agamben’s interpretation, does, however, exclude him from belonging to the ‘class of study’. Bartleby’s exclusion leads to the discovery of an unmentioned member of the ‘class of study’: Eros. The surprising absence of Eros dissolves, however, once he (...) is recuperated as the image of ‘The idea of the work’. Bartleby’s exclusion and Eros’s absent inclusion and presence as the ‘The idea of the work’ not only demonstrate the close relation between study and work, but also explain Agamben’s considerations on the connection between study and the nature of his own work. The article concludes with a call for the remaining importance of Agamben’s festina lente, the rhythm of study, within the broader context of our contemporary university institutions. Once the incessant shuttling between passion and action has been called to a halt—in favour of one of the two extremities—study becomes impossible. (shrink)

У статті проаналізований медіа-простір, в якому православні та греко-католицька конфесії представлені постатями своїх речників. Спікерство в релігійних організаціях – це специфічний вид соціальних комунікацій, адже пріоритетною в них є керигма, тобто місійна проповідь. Головна мета статті – через аналіз вузлових повідомлень провідних речників православних та греко-католицькоїконфесій окреслити роль цих постатей у соціальних комунікаціях. Методологія. Реалізація мети та завдань статті зумовила застосування емпіричного та теоретичного методів. Зокрема,спостереження як емпіричний метод застосовуємо, щоб виокремити постаті провідних речників, їхні вузловімедіа-повідомлення. Метод порівняння використовуємо, щоб (...) дослідити комунікаційний дискурс кожної з церков в особі їхніх речників. Теоретичні методи дослідження дають змогу заглибитись у комунікаційне поле дискурсів. Розглядаючи окремі вектори комунікації між церквою та суспільством, використовуємо теорію дискурсу Е. Лакло і Ш. Муфф, де основою є боротьба дискурсів, а також теорію медій Максвела Мак-Комбса, що рольЗМІпоказує через аналіз їхньої дії та суспільних наслідків. В основі дослідження представлено такі завдання: проаналізувати громадську думку стосовно провідних речників конфесій; визначити, яку роль відіграють речники в генеруванні діалогу між цервою та суспільством; з’ясувати основні концептуальні повідомлення, які артикулюють речники; проаналізувати головні теми комунікаційного діалогу, а через них позиціювання цихцерков у медіа-просторі. Наукова новизна дослідження у виявленніролі речників православних і греко-католицької конфесій через їхні засадничі повідомлення у соціальних комунікаціях. Це дозволяє зробити висновок, що за період незалежності України з її конфесійного простору виокремилися авторитетні речники, які забезпечують для своїх церков ефективні соціальні комунікації. Православне середовище представлене низкою постатей речників, які артикулюють та уособлюють ті чи інші стратегічні вектори розвитку конфесій. Зокрема, УПЦ КПдіє як національна церква, активно проголошуючи необхідність для Української держави єдиної Помісної православної церкви. Патріарх Філарет у суспільній свідомості постає в образі загальнонаціонального релігійного лідера. Прес-секретар УПЦ КП Євстратій Зоря займається активним викриттям політики «русскогомира», донесенням через європейські структури до світової громадськості української позиції щодо релігійних аспектів воєнних дій.Середовище УПЦ МП сегментоване на два протилежних табори: проукраїнський та проросійський. Митрополит Володимир і прот. Георгій Коваленко як провідні речники конфесії демонструють позицію до автономії від РПЦ, розвиток її як української церкви, що прагне певної модернізації. Водночас митрополит Онуфрій уособлює консервативний і проросійський вектор розвитку УПЦ МП у парадигмі «русского мира». Греко-католики в інформаційному просторі України представлені постатями своїх речників кардинала Любомира Гузараі верховного архиєпископа Святослава, які завдяки своїй ґрунтовній освіті, духовному й церковному досвіду, активній громадянській позиції, відкритості є лідерами думок не тільки для греко-католицької аудиторії, але й загальноукраїнської. (shrink)

Last year, the anniversary of all Christianity, witnessed a number of significant events caused by a new interest in understanding the problem of the unity of the Christian Church on the turn of the millennium. Due to the confidentiality of Ukraine, some of these events have or will have an immediate impact on Christianity in Ukraine and on the whole Ukrainian society as a whole. Undoubtedly, the main event, or more enlightened in the press, is a new impetus to the (...) unification of the UOC-KP and the UAOC. But we would like to focus on two documents relating to the problem of Christian unity, the emergence of which was almost unnoticed by the wider public. But at the same time, these documents are too important as they outline the future policy of other Christian denominations by two influential Ukrainian christian churches - the Russian Orthodox Church and the Ukrainian Greek Catholic Church. These are the "Basic Principles of the attitude of the Russian Orthodox Church to the" I ", adopted by the Anniversary Bishops' Council of the Russian Orthodox Church, and the Concept of the Ecumenical Position of the Ukrainian Greek Catholic Church, adopted by the Synod of the Bishops of the UGCC. It is clear that the theme of the second document is wider, but at the same time, ecumenism, unification is impossible without solving the problem of relations with others, which makes it possible to compare the approaches laid down in the mentioned documents to the building of relations with other Christian confessions. (shrink)

The purpose of the article is to analyze different aspects of information activity through the prism of television content of Christian denominations. The information product of the Christian television space is researched; functional, genre and content specifics are studied. Methodology is systematic, comparative, axiological methods and approaches that allow deeply penetrate into the confessional information environment of the television section. Information activities of Ukraine Christian denominations are represented in societal, praxeological segment. The specific of Christian television genre and content was (...) analyzed. It is characterized by the use of this media channel as a mean of implementing its own religious mission, information and interpretation of denominations position on various aspects of society and human life to the believers and the general public, a powerful spiritual enlightenment. It has been found that the Christian television space contributes to deepening of individualistic and sometimes consumeristic approaches of modern man to religion, to own choice of religion and religious practices. (shrink)

In the article of Viktoria Zaporozhets «Main aspects of external church relations of UAOC in the 90’s. XX century» from the religious-scientific point of view is carried out a comprehensive analysis of the institutionalization of the UAOC in the 90's of the twentieth century in the context of her external-church relation. It is noted that inter-church relations of the UAOC during the specified period of her existence can be characterized as two-vector. It is emphasized that the first vector is due (...) to the processes of interaction between the UAOC and the UOC-KP and the UOC that took place at the canonical councils / sessions of commissions, and the second vector is related to the fact that the UAOC tried to gain the canonical status of the Ecumenical Patriarch through the diocese of Canada and the United States. At the same time it is noted that although there were diplomatic inter-Orthodox relations of the UAOC, nevertheless there were temple seizures from each other. It is proved that the church-state relations of the UAOC in this period can be characterized as stable, since it was granted the right to perform services and own property, to open Sunday schools, to freely serve services in the Ukrainian language, although sometimes it was possible to find a negative attitude to this religious organization from the side of power. (shrink)

Is it possible and whether it is necessary to consider the events of the inter-church and inter-church Orthodox life of Ukraine through the prism of national security? What are the pain points in relations between the Ukrainian state and the Orthodox Churches? Does the legislation in Ukraine regulate state-church relations in Ukraine and whether it is Ukrainian-centric? These and other issues were the subject of consideration of the Expert Round Table on "Fighting Identities in Orthodoxy of Ukraine after the" Revolution (...) of Dignity ": an aspect of national security", which took place in Kyiv on July 1, 2014. The organizers of the event were the All-Ukrainian Society "Prosvita" named after Taras Shevchenko and the Ukrainian Association of Religious Studies. In the work of the Round Table, in addition to the representatives of the organizers of this conference, experts from the UOC-KP, UOC-MP, the All-Ukrainian Orthodox Brotherhood of Andriy Pervozvannogo of the UOC-KP, scholars and public figures from different cities and regions of the country, and other interested persons took part. (shrink)

One of the most intriguing claims in Sven Rosenkranz’s Justification as Ignorance is that Timothy Williamson’s celebrated anti-luminosity argument can be resisted when it comes to the condition ~K~KP—the condition that one is in no position to know that one is in no position to know P. In this paper, I critically assess this claim.

I am reading an April 4 issue of the newspaper "Day" in an interview with the Director of the UOC of the Moscow Patriarchate Anthony. It reminds me of a well-known Ukrainian national comparison: it is yorking like a scar on a skillet. The Bishop's questions sound clear: Does your Church condemn the aggression of Russia and its annexation of Crimea? Why did not you condemn the aggressive actions of Russia Your Moscow Patriarch Kirill? No answer. The Church of the (...) Kyiv Patriarchate or the Ukrainian Greek Catholic Church in the mouth of its predecessors has clearly said: We have aggression against Muscovy, we condemn it. Even my fellow countryman, the Cherkasy eparch of the UOC MP Metropolitan Sofroni called Putin a bandit. And Bishop Antony spoke so much that the elephant could be wrapped up in his printed interview, but the conqueror of the invader still failed. Therefore, the authorities of the Orthodox Church of Moscow jurisdiction do not hear the Ukrainian people, which all are inclined to go to the ranks of the National Guard to defend our independence. Even I in my 77 agreed to this. (shrink)

The Dialectica-style functional interpretation of Kripke-Platek set theory with infinity ( $\hbox{\sf KP} \omega$ ) given in [1] uses a choice functional (which is not a definable set function of ( $hbox{\sf KP} \omega$ ). By means of a Diller-Nahm-style interpretation (cf. [4]) it is possible to eliminate the choice functional and give an interpretation by set functionals primitive recursive in $x\mapsto\omega$ . This yields the following characterization: The class of $\Sigma$ -definable set functions of $\hbox{\sf KP} \omega$ coincides with (...) the collection of set functionals of type 1 primitive recursive in $x\mapsto \omega$. (shrink)

The subject of this paper is a characterization of the $\Sigma_1$ -definable set functions of Kripke-Platek set theory with infinity and a uniform version of axiom of choice: $KP\omega+(uniform\;AC)$ . This class of functions is shown to coincide with the collection of set functionals of type 1 primitive recursive in a given choice functional and $x\mapsto\omega$ . This goal is achieved by a Gödel Dialectica-style functional interpretation of $KP\omega+(uniform\;AC)$ and a computability proof for the involved functionals.

The Dialectica-style functional interpretation of Kripke-Platek set theory with infinity (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\hbox{\sf KP} \omega$\end{document}) given in [1] uses a choice functional (which is not a definable set function of (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $hbox{\sf KP} \omega$\end{document}). By means of a Diller-Nahm-style interpretation (cf. [4]) it is possible to eliminate the choice functional and give an interpretation by set functionals primitive recursive in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} (...) \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $x\mapsto\omega$\end{document}. This yields the following characterization: The class of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\Sigma$\end{document}-definable set functions of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\hbox{\sf KP} \omega$\end{document} coincides with the collection of set functionals of type 1 primitive recursive in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $x\mapsto \omega$\end{document}. (shrink)

Résumé Chez Samuel Beckett, François Morellet et KP Brehmer, l’art de la contrainte impose une trame formelle et logique pour mieux la trahir – l’altérer, la révéler –, renouvelant au passage l’économie de l’œuvre et son statut. Dans une double tradition littéraire et plastique, la mise au dehors du geste créateur et l’apparente désaffection des systèmes choisis produisent autant d’interférences symptomatiques dans l’œuvre et dans son contexte. Cet abandon agit comme le moyen paradoxal d’impliquer l’affect et d’ouvrir l’œuvre à des (...) résonances nouvelles. (shrink)

In this paper we introduce a notation system for the infinitary derivations occurring in the ordinal analysis of KP + Π₃-Reflection due to Michael Rathjen. This allows a finitary ordinal analysis of KP + Π₃-Reflection. The method used is an extension of techniques developed by Wilfried Buchholz, namely operator controlled notation systems for RS∞-derivations. Similarly to Buchholz we obtain a characterisation of the provably recursive functions of KP + Π₃-Reflection as <-recursive functions where < is the ordering on Rathjen's ordinal (...) notation system J(K). Further we show a conservation result for $\Pi _{2}^{0}$-sentences. (shrink)

Scepticism does not argue that no one knows to avoid self-referential refutation. It falls back to arguing that no one knows that anyone knows, hence simply that no one knows, in accordance with the principle Kp iff KKp. This principle, however, is not available to the sceptic. He is stuck with -KKp without access to -Kp. The sceptic is thus no threat to the sort of knowledge that like Moore we all claim to have.

Let KP- be the theory resulting from Kripke-Platek set theory by restricting Foundation to Set Foundation. Let G: V → V (V:= universe of sets) be a ▵0-definable set function, i.e. there is a ▵0-formula φ(x, y) such that φ(x, G(x)) is true for all sets x, and $V \models \forall x \exists!y\varphi (x, y)$ . In this paper we shall verify (by elementary proof-theoretic methods) that the collection of set functions primitive recursive in G coincides with the collection of (...) those functions which are Σ1-definable in KP- + Σ1-Foundation + ∀ x ∃!yφ (x, y). Moreover, we show that this is still true if one adds Π1-Foundation or a weak version of ▵0-Dependent Choices to the latter theory. (shrink)

Lascar described E KP as a composition of E L and the topological closure of E L (Casanovas et al. in J Math Log 1(2):305–319). We generalize this result to some other pairs of equivalence relations. Motivated by an attempt to construct a new example of a non-G-compact theory, we consider the following example. Assume G is a group definable in a structure M. We define a structure M′ consisting of M and X as two sorts, where X is an (...) affine copy of G and in M′ we have the structure of M and the action of G on X. We prove that the Lascar group of M′ is a semi-direct product of the Lascar group of M and G/G L . We discuss the relationship between G-compactness of M and M′. This example may yield new examples of non-G-compact theories. (shrink)

Working in Z + KP, we give a new proof that the class of hereditarily finite sets cannot be proved to be a set in Zermelo set theory, extend the method to establish other failures of replacement, and exhibit a formula Φ(λ, a) such that for any sequence $\langle A_{\lambda} \mid \lambda \text{a limit ordinal} \rangle$ where for each $\lambda, A_{\lambda} \subseteq ^{\lambda}2$ , there is a supertransitive inner model of Zermelo containing all ordinals in which for every λ A (...) λ = {α ∣Φ(λ, a)}. (shrink)

Working in Z + KP, we give a new proof that the class of hereditarily finite sets cannot be proved to be a set in Zermelo set theory, extend the method to establish other failures of replacement, and exhibit a formula $\Phi$ such that for any sequence $\langle A_{\lambda} \mid \lambda \text{a limit ordinal} \rangle$ where for each $\lambda, A_{\lambda} \subseteq ^{\lambda}2$, there is a supertransitive inner model of Zermelo containing all ordinals in which for every $\lambda A_{\lambda} = \{\alpha (...) \mid\Phi\}$. (shrink)

The general verificationist thesis says that What is true can be known or formally: φ → ◊Kφ VT Fitch's argument trivializes this principle. It uses a weak modal epistemic logic to show that VT collapses truth and knowledge, by taking a clever substitution instance for φ: P ∧ ¬KP → ◊ K(P ∧ ¬KP) Then we have the following chain of three conditionals (a) ◊ K(P ∧ ¬KP) → ◊ (KP ∧ K¬KP) in the minimal modal logic for the knowledge (...) operator K, (b) ◊ (KP ∧ K¬KP) → ◊ (KP ∧¬KP) in the modal logic T, and finally (c) ◊ (KP ∧¬KP) → ⊥ in the minimal modal logic for. (shrink)

The naive anti-realist holds the following principle: (◊K) All truths are knowable. This unrestricted generalization (◊K), as is now well known, falls prey to Fitch’s Paradox (Fitch 1963: 38, Theorem 1). It can be used as the only suspect principle, alongside others that cannot be impugned, to prove quite generally, and constructively, that the set {p, ¬Kp} is inconsistent (Tennant 1997: 261). From this it would follow, intuitionistically, that any proposition that is never actually known to be true (by anyone, (...) at any time) is false; and it would follow, classically, that every truth is known (by someone, at some time). (shrink)

Nghiên cứu này được thực hiện để tìm hiểu liệu các nguồn thông tin ảnh hưởng đến quyết định đầu tư của nhà đầu tư có ảnh hưởng đến sự sợ hãi của họ khi khủng hoảng xảy ra hay không? Nghiên cứu đã sử dụng phương pháp phân tích Bayesian Mindsponge Framework (BMF) trên bộ dữ liệu từ 1,526 nhà đầu tư Trung Quốc và Việt Nam. Kết quả nghiên cứu chỉ ra rằng, các nhà đầu tư tiếp cận (...) các loại thông tin khác nhau khi đưa ra quyết định đầu tư sẽ ảnh hưởng đến tần suất phản ứng sợ hãi khác nhau. Cụ thể, các nhà đầu tư tham khảo thông tin từ chuyên gia hoặc tự phân tích khi đưa ra quyết định đầu tư ít bị đóng băng (biểu hiện của tâm lý sợ hãi) hơn trong thời kỳ thị trường sụt giảm. Ngược lại, những người đưa ra quyết định đầu tư dựa trên thông tin từ người quen hay bạn bè và trực giác sẽ bị đóng băng thường xuyên hơn. -/- [English Abstract] This study was conducted to explore whether the sources of information priority during decision-making contribute to their fear reactions during crises. The research utilized the Bayesian Mindsponge Framework (BMF) analytics on data collected from 1,526 investors in China and Vietnam. The study results indicated that investors prioritizing different types of information when making investment decisions would have different frequency of fear reactions. Specifically, investors who prioritized information from experts or conducted self-analysis when making investment decisions experienced less freezing (an expression of psychological fear) during market downturns. Conversely, those who based their investment decisions on information from acquaintances, friends, and intuition tended to experience freezing more frequently. (shrink)

Can we turn the screw on counter-examples to the KK principle (that if one knows that P, one knows that one knows that P)? The idea is to construct cases in which one knows that P, but the epistemic status for one of the proposition that one knows that P is much worse than just one’s not knowing it. Of course, since knowledge is factive, there can’t be cases in which one knows that P and knows that one doesn’t know (...) that P (we can’t strengthen ¬KKp to K¬Kp)! If we can construct such cases, we may be able to use them to understand some puzzling epistemic phenomena. (shrink)

In this paper we introduce a recursive notation system O(Π 3 ) of ordinals. An element of the notation system is called an ordinal diagram. The system is designed for proof theoretic study of theories of Π 3 -reflection. We show that for each $\alpha in O(Π 3 ) a set theory KP Π 3 for Π 3 -reflection proves that the initial segment of O(Π 3 ) determined by α is a well ordering. Proof theoretic study for such theories (...) will be reported in [4]. (shrink)

Rosenkranz (2021) offered a logic and a detailed account of justification, according to which justification that p can be analyzed as a form of second-level ignorance: ¬K¬Kp. An intuition behind the analysis is that the justified subject has the potential, at least in a nearby world, to either come to know p or come to know ¬Kp. However, given Rosenkranz’s hyperintensional semantics for modeling knowledge states, we can always construct, out of an ¬K¬K-agent’s knowledge state, epistemic possibilities that prohibit the (...) agent from having that potential. This shows that Rosenkranz’s analysis is still insufficient for carrying all the epistemic weight underlying the notion of justification. A better analysis would require a deeper look into an agent’s knowledge structure and its involved modalities, which could be a lot more complex than what the ¬K¬K rule tells us. (shrink)

1 There is a Standard Objection to the idea that concepts might be prototypes (or exemplars, or stereotypes): Because they are productive, concepts must be compositional. Prototypes aren't compositional, so concepts can't be prototypes (see, e.g., Margolis, 1994).2 However, two recent papers (Osherson and Smith, 1988; Kamp and Partee, 1995) reconsider this consensus. They suggest that, although the Standard Objection is probably right in the long run, the cases where prototypes fail to exhibit compositionality are relatively exotic and involve phenomena (...) which any account of compositionality is likely to find hard to deal with; for example, the effects of quantifiers, indexicals, contextual constraints, etc. KP are even prepared to indulge a guarded optimism: "... when a suitably rich compositional theory... is developed, prototypes will be seen ... as one property among many which only when taken altogether can support a compositional theory of combination" (p.56). In this paper, we argue that the Standard Objection to prototype theory was right after all: The problems about compositionality are insuperable in even the most trivial sorts of examples; it is therefore as near to certain as anything in cognitive science ever gets that the structure of concepts is not statistical. Theories of categorization, concept acquisition, lexical meaning and the like, which assume the contrary simply don't work. We commence with a general discussion of the constraints that an account of concepts must meet if their compositionality is to explain their productivity. We'll then turn to a criticism of proposals that OS2 and KP make for coping with some specific cases. (shrink)

One of the open problems in the philosophy of information is whether there is an information logic (IL), different from epistemic (EL) and doxastic logic (DL), which formalises the relation “a is informed that p” (Iap) satisfactorily. In this paper, the problem is solved by arguing that the axiom schemata of the normal modal logic (NML) KTB (also known as B or Br or Brouwer’s system) are well suited to formalise the relation of “being informed”. After having shown that IL (...) can be constructed as an informational reading of KTB, four consequences of a KTB-based IL are explored: information overload; the veridicality thesis (Iap → p); the relation between IL and EL; and the Kp → Bp principle or entailment property, according to which knowledge implies belief. Although these issues are discussed later in the article, they are the motivations behind the development of IL. (shrink)

In his Knowledge and Belief (1962), Hintikka establishes his system of epistemic logic with the KK (Knowing that One Knows, in symbols, Kp→KKp) principle (KK for short). However, his system of epistemic logic and the KK principle are grounded upon his strong notion of knowledge, which requires that knowledge is infallible, that is, it makes further inquiry pointless, and becomes ‘discussion-stopper’; knowledge implies truth, to wit, cognitive agents will not be mistaken in their knowledge; cognitive agents will be ‘perfect logicians’, (...) i.e. they have infinitive capability of logical inference. Hintikka calls the argument for KK from the strong notion of knowledge as the ‘transcendental argument’ for KK. Obviously, the strong notion of knowledge is far away from our ordinary conception of knowledge; based on such a strong sense of knowledge, epistemic logic has met the problem of logical omnipotence, and is difficult to apply in our ordinary cognitive practice. Moreover, there is no close connection of the KK principle with internalism or externalism. (shrink)

In this article we study several reduction principles in the context of Simpson’s set theory ATR0S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ATR_{0}^{S}$$\end{document} and Kripke-Platek set theory KP (with infinity). Since ATR0S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ATR_{0}^{S}$$\end{document} is the set-theoretic version of ATR0 there is a direct link to second order arithmetic and the results for reductions over ATR0S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ATR_{0}^{S}$$\end{document} are as expected and more or less (...) straightforward. However, over KP we obtain several interesting new results and are lead to some open questions. (shrink)

We will study patterns which occur when considering how Σ 1 -elementary substructures arise within hierarchies of structures. The order in which such patterns evolve will be seen to be independent of the hierarchy of structures provided the hierarchy satisfies some mild conditions. These patterns form the lowest level of what we call patterns of resemblance . They were originally used by the author to verify a conjecture of W. Reinhardt concerning epistemic theories 449–460; Ann. Pure Appl. Logic, to appear), (...) but their relationship to axioms of infinity and usefulness for ordinal analysis were manifest from the beginning. This paper is the first part of a series which provides an introduction to an extensive program including the ordinal analysis of set theories. Future papers will conclude the introduction and establish, among other things, that notations we will derive from the patterns considered here represent the proof-theoretic ordinal of the theory KPℓ 0 or, equivalently, Π 1 1 −CA 0. (shrink)

The paper takes as its starting point the observation that people can be led to retract knowledge claims when presented with previously ignored error possibilities, but offers a noncontextualist explanation of the data. Fallibilist epistemologies are committed to the existence of two kinds of Kp -falsifying contingencies: (i) Non-Ignorable contingencies [NI-contingencies] and (ii) Properly-Ignorable contingencies [PI-contingencies]. For S to know that p, S must be in an epistemic position to rule out all NI-contingencies, but she need not be able to (...) rule out the PI-contingencies. What is required vis-à-vis PI-contingencies is that they all be false . In mentioning PI-contingencies, an interlocutor can lead S mistakenly to think that these contingencies are NI-contingencies, when in fact they are not. Since S cannot rule out these newly mentioned contingencies and since she mistakenly takes them to be NI-contingencies , it is quite natural that she retract her earlier knowledge claim. In short, mentioning NI-contingencies creates a distortion effect. It makes S think that the standards for knowledge are higher than they actually are, which in turn explains why she mistakenly thinks she lacks knowledge. Conclusion: The primary linguistic data offered in support of contextualism can be explained without resorting to contextualism. (shrink)